Liang, Jin; Xiao, Ti-Jun Solutions to abstract integral equations and infinite delay evolution equations. (English) Zbl 1236.45009 Bull. Belg. Math. Soc. - Simon Stevin 18, No. 5, 793-804 (2011). The authors first establish general criteria to judge the existence of Lipschitz continuous solutions to the Cauchy problem for integral equations with infinite delay in Banach spaces. Then they give new existence theorems of strong and classical solutions to the Cauchy problem for some evolution equations with infinite delay by means of these criteria. Reviewer: Som Prakash Goyal (Jaipur) Cited in 1 Document MSC: 45N05 Abstract integral equations, integral equations in abstract spaces 47D06 One-parameter semigroups and linear evolution equations Keywords:Lipschitz continuity; Cauchy problem; abstract integral equation; infinite delay evolution equation; infinite delay; Banach spaces PDFBibTeX XMLCite \textit{J. Liang} and \textit{T.-J. Xiao}, Bull. Belg. Math. Soc. - Simon Stevin 18, No. 5, 793--804 (2011; Zbl 1236.45009) Full Text: Euclid